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http://functions.wolfram.com/13.07.23.0001.01
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Sum[MoebiusMu[k] Floor[x/k], {k, 1, x}] == 1 /; x >= 1
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "x"], RowBox[List[RowBox[List["MoebiusMu", "[", "k", "]"]], " ", RowBox[List["Floor", "[", FractionBox["x", "k"], "]"]]]]]], "\[Equal]", "1"]], "/;", RowBox[List["x", "\[GreaterEqual]", "1"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> x </mi> </munderover> <mrow> <mrow> <semantics> <mi> μ </mi> <annotation encoding='Mathematica'> TagBox["\[Mu]", MoebiusMu] </annotation> </semantics> <mo> ( </mo> <mi> k </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⌊ </mo> <mfrac> <mi> x </mi> <mi> k </mi> </mfrac> <mo> ⌋ </mo> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mn> 1 </mn> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> ≥ </mo> <mn> 1 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> x </ci> </uplimit> <apply> <times /> <apply> <ci> MoebiusMu </ci> <ci> k </ci> </apply> <apply> <floor /> <apply> <times /> <ci> x </ci> <apply> <power /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <geq /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "1"]], "x_"], RowBox[List[RowBox[List["MoebiusMu", "[", "k", "]"]], " ", RowBox[List["Floor", "[", FractionBox["x_", "k"], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["1", "/;", RowBox[List["x", "\[GreaterEqual]", "1"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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